Laissez Faire

Letting Life Lead

Writes and Wrongs #7: Subtraction (Regrouping / Decomposition / Borrowing) For the Parents

I am not a math genius.   I am quite average in skill.  I know this series started with writing, but I figured why not share some basic math skills.    I was not taught understanding in school — just the steps — so I had had to re-teach myself in my old age quite a few times over the growing years.  And, of course, the best way to learn something and not lose it is to practice and to teach it to someone else.


Subtraction with Borrowing (also known as Regrouping or Decomposition)

When you do a subtraction with borrowing with the standard algorithm, you are using a series of steps and short cuts to compute an answer from right to left.   Now, this method works.  No doubt!  However, you must have a strong understanding of place value and what you are actually doing or else you are just following steps.  This makes it hard to figure out common mistakes, such as why you have trouble subtracting from a number with a lot of zeros.

While this method works very well on paper, it can get quite messy.   It is also quite difficult to teach and learn if someone doesn’t have a firm grasp of place value or is not comfortable with re-writing numbers (2 + 5 is the same value as 3 + 4).  Not only that, but it is NOT a method you would use for “in your head” calculation.  All those numbers to “hold in you head” when you regroup/borrow is difficult.  You also need to be comfortable doing subtraction facts higher than 10 such as 15 – 8 and 12 – 9.

Regrouping - Decomposition - Borrowing Demonstration


You may have done this method efficiently over the years without ever knowing that you aren’t actually borrowing “1” ever.  That’s just a short hand notation.   If you look at the full shortcut above, it looks like I have been using values 7, 12, and 12 when in fact those values mean 700 120 and 12.    Add them up and you get 832.      You are always borrowing values of 10, 100, 1000, etc.  depending on how big your number is.  This is why knowing place value is very important and why it is very common for children and adults to make errors when the top number has zeros.      If you ask me, a funny quirk of this method (and this is the method that is ingrained in my brain) is that you can get the answer without ever understanding what the heck it is you are doing!

Did you know how borrowing/regrouping worked?   Do you understand now?  Can you do subtraction in your head this way with numbers bigger than two digit values?


2 comments on “Writes and Wrongs #7: Subtraction (Regrouping / Decomposition / Borrowing) For the Parents

  1. pauljgies
    March 9, 2016

    I can’t possibly LIKE this enough. I teach math for elementary teachers (among other things) at the University of Maine at Farmington, and we talk a lot about why different algorithms work. One thing I didn’t know until just a few years ago is that Europeans learn to do this a different way… or two different ways, for example the so-called Austrian algorithm, which is just a streamlined version of the above. And here’s a lovely link…

    A different version has you adding to the bottom number instead of borrowing from the top, so that:

    5 2
    – 2 8

    5 12 (“fifty twelve”)
    – 3 8

    = 2 4 (yes!)

    And then there’s this oddity…

    We adopt the principle that teachers should know several algorithms for any given operation, because each child should become totally proficient at some algorithm, though it doesn’t matter which one.


    Liked by 1 person

    • Laissez Faire
      March 9, 2016

      Thank you! I have been teaching myself the Austrian algorithm. I have recently discovered the partial products for subtraction (I felt a little duh moment about that). My favorite though is the 9 plus one method.


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